Asymptotics, Turán inequalities, and the distribution of the BG-rank and 2-quotient rank of partitions

Andrew Baker, Joshua Males

Let $j,n$ be even positive integers, and let ${\overline{p}}_j(n)$ denote the number of partitions with BG-rank $j$, and ${\overline{p}}_j(a,b;n)$ to be the number of partitions with B…